2019年华中科技大学博士研究生入学《偏微分方程》考试大纲

华中科技大学博士研究生入学《偏微分方程》考试大纲

（代码：2296）

1、考试科目：《偏微分方程》

2、答题方式：闭卷、笔试

3、答题时间：180分钟

4、总    分：100分

5、考试内容

A．Four Important Linear PDEs

(1) Transport equation     (2) Laplace equation

(3) Heat equation          (4) Wave equation

B. Nonlinear First-Order PDE

(1) Complete integrals, envelops     (2) Characteristics

(3) Hamilton-Jacobi equation         (4) Conservation laws

C. Other Ways to Represent Solutions

(1) Separation of Variables    (2) Similarity Solutions

(3) Transform methods          (4) Converting nonlinear into linear PDE

(5) Asymptotics                (6) Power Series

D. Sobolev Spaces

(1) Holder spaces     (2) Sobolev spaces     (3) Approximation

(4) Extension         (5) Traces             (6) Sobolev inequalities

(7) Compactness       (8) Additional topics  (9) Other spaces of functions